Hans Föllmer

Efficient hedging: Cost versus shortfall risk

Abstract. An investor faced with a contingent claim may eliminate risk by (super-) hedging in a financial market. As this is often quite expensive, we study partial hedges which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal probability, given a capital constraint. Here we look for strategies which minimize the shortfall risk defined as the expectation of the shortfall weighted by some loss function. The resulting efficient hedges allow the investor to interpolate in a systematic way between the extremes of no hedge and a perfect (super-) hedge, depending on the accepted level of shortfall risk.

The financial crisis and the systemic failure of academic economics

The economics profession appears to have been unaware of the long build-up to the current worldwide financial crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics. We trace the deeper roots of this failure to the professions focus on models that, by design, disregard key elements driving outcomes in real-world markets. The economics profession has failed in communicating the limitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists undertake, as well as for the establishment of an ethical code that would ask economists to understand and communicate the limitations and potential misuses of their models.

Robust Preferences and Convex Measures of Risk

We prove robust representation theorems for monetary measures of risk in a situation of uncertainty, where no probability measure is given a priori. They are closely related to a robust extension of the Savage representation of preferences on a space of financial positions which is due to Gilboa and Schmeidler. We discuss the problem of computing the monetary measure of risk induced by the subjective loss functional which appears in the robust Savage representation.

Optional Decomposition and Lagrange Multipliers

Abstract. Let

Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading

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Robust Preferences and Robust Portfolio Choice

be the set of equivalent martingale measures for a given process

ENTROPIC RISK MEASURES: COHERENCE VS. CONVEXITY, MODEL AMBIGUITY AND ROBUST LARGE DEVIATIONS

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Quadratic Covariation and an Extension of Itô's Formula@@@Quadratic Covariation and an Extension of Ito's Formula

, and let

American Options, Multi–armed Bandits, and Optimal Consumption Plans: A Unifying View

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On the Global Markov Property

be a process which is a local supermartingale with respect to any measure in